七、图像边缘检测之 Sobel、Scharr、拉普拉斯算子、Canny

迷南。 2023-06-14 09:29 2阅读 0赞

**目录**

一、Sobel

1、理论基础

2、Sobel算子函数及使用

（1）Sobel算子

（2）代码实例

二、Scharr

三、Sobel和Scharr比较

四、Laphlacian

五、Canny边缘检测

1、原理

2、代码实例

--------------------

# 一、Sobel #

## 1、理论基础 ##

**p5点处的水平方向梯度计算**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70][]

**p5点处竖直方向的梯度**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 1][]

**图像的每一个像素的横向及纵向灰度值通过以下公式结合，来计算该点灰度的大小：**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 2][]

但是有时候，计算sqrt(Gx2+Gy2)不太好算，故我们做一个简化：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 3][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 4][]

## 2、Sobel算子函数及使用 ##

### **（1）Sobel算子** ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 5][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 6][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 7][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 8][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 9][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 10][]

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![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 12][]

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![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 15][]

### （2）代码实例 ###

# encoding: utf-8
    
    import cv2
    import matplotlib.pyplot as plt
    import math
    import copy
    import numpy as np
    
    def show_img(name="test",img=None):
        plt.figure()
        plt.imshow(img)
        plt.title(name)
        plt.show()
    
    path = r"lena.jpg"
    img = cv2.imread(path)
    gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
    # 1
    #计算 深度-1，x方向梯度 1，即目标图像和原始图像都是256色域的图像，y方向梯度同理
    # 出现问题：会被截断，导致计算不出图像左侧的边界，
    soble_x1 = cv2.Sobel(gray,-1,1,0)
    # show_img(img=soble_x1)
    # 2
    # 解决1中问题，y方向梯度同理
    soble_x2 = cv2.Sobel(gray,cv2.CV_64F,1,0)
    soble_x2 = cv2.convertScaleAbs(soble_x2)
    # show_img(img=soble_x2)
    # 3
    #同时计算x 和y 方向梯度（边界）,若同时计算 两个方向梯度边界，这种方式比较好
    soble_x3 = cv2.Sobel(gray,cv2.CV_64F,1,0)
    soble_y3 = cv2.Sobel(gray,cv2.CV_64F,0,1)
    soble_x3 = cv2.convertScaleAbs(soble_x3)
    soble_y3 = cv2.convertScaleAbs(soble_y3)
    soble_xy3 = cv2.addWeighted(soble_x3, 0.5, soble_y3, 0.5, 0)
    # show_img(img=soble_xy)
    # 4
    #同时计算 x 和 y 方向梯度，但是这种方式计算出的结果不好
    #出现问题：结果不好，最好使用 3 中的方式
    soble_xy4 = cv2.Sobel(gray,cv2.CV_64F,1,1)
    soble_xy4 = cv2.convertScaleAbs(soble_xy4)
    show_img(img=soble_xy4)

# 二、Scharr #

sobel算子不怎么用，一般scharr算子运用的比较多

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 16][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 17][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 18][]

# encoding: utf-8
    
    import cv2
    import matplotlib.pyplot as plt
    import math
    import copy
    import numpy as np
    
    def show_img(name="test",img=None):
        plt.figure()
        plt.imshow(img)
        plt.title(name)
        plt.show()
    
    path = r"lena.jpg"
    img = cv2.imread(path)
    gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
    # 1
    #计算 深度-1，x方向梯度 1，即目标图像和原始图像都是256色域的图像，y方向梯度同理
    # 出现问题：会被截断，导致计算不出图像左侧的边界，
    scharr_x1 = cv2.Scharr(gray,-1,1,0)
    # show_img(img=scharr_x1)
    # 2
    # 解决1中问题，y方向梯度同理
    scharr_x2 = cv2.Scharr(gray,cv2.CV_64F,1,0)
    scharr_x2 = cv2.convertScaleAbs(scharr_x2)
    # show_img(img=scharr_x2)
    # 3
    #同时计算x 和y 方向梯度（边界）,若同时计算 两个方向梯度边界，这种方式比较好
    scharr_x3 = cv2.Scharr(gray,cv2.CV_64F,1,0)
    scharr_y3 = cv2.Scharr(gray,cv2.CV_64F,0,1)
    scharr_x3 = cv2.convertScaleAbs(scharr_x3)
    scharr_y3 = cv2.convertScaleAbs(scharr_y3)
    scharr_xy3 = cv2.addWeighted(scharr_x3, 0.5, scharr_y3, 0.5, 0)
    show_img(img=scharr_xy3)
    # 4
    #同时计算 x 和 y 方向梯度，但是这种方式计算出的结果不好
    #出现问题：报错，无法执行，无法通过编译器编译
    scharr_xy4 = cv2.Scharr(gray,cv2.CV_64F,1,1)#
    scharr_xy4 = cv2.convertScaleAbs(scharr_xy4)
    # show_img(img=scharr_xy4)
    print("===========可以使用Sobel计算Scharr梯度，即通过调节Soble最后参数达到Scharr的效果=============")
    # 调节最后一个参数，-1表示使用和Scharr算子相同的算法计算
    scharr_x5 = cv2.Sobel(gray,cv2.CV_64F,1,0,-1)
    scharr_y5 = cv2.Sobel(gray,cv2.CV_64F,0,1,-1)
    scharr_x5 = cv2.convertScaleAbs(scharr_x5)
    scharr_y5 = cv2.convertScaleAbs(scharr_y5)

# 三、Sobel和Scharr比较 #

*  kernel大小一样，故计算量一样。
 *  scharr算子临近像素的权重更大，故精确度更高。
 *  **对比两种算子的处理效果。发现scharr算子能计算出更小的梯度变化**

# 四、Laphlacian #

拉普拉斯算子可以使用**二阶导数的形式定义**，可假设其离散实现类似于二阶Sobel导数，事实上，OpenCV在计算拉普拉斯算子时直接调用Sobel 算子。

![20191119233911266.png][]

Laplacian算子：**图像中的边缘区域，像素值会发生“跳跃”，对这些像素求导，在其一阶导数在边缘位置为极值，这就是Sobel算子使用的原理——极值处就是边缘。**

每个求导数的方法都是使用Sobel求导方法,如果 ksize=1，那么会使用下面核函数进行滤波.

![20191119234009424.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 19][]

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这里只是处理单通道的灰度图像，彩色的三通道的图像同理。

# 五、Canny边缘检测 #

## 1、原理 ##

参考： [Canny算子原理][Canny]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 24][]

Canny边缘检测算法可以分为以下5个步骤：

1) 使用高斯滤波器，以平滑图像，滤除噪声。

2) 计算图像中每个像素点的梯度强度和方向。

3) 应用非极大值（Non-Maximum Suppression）抑制，以消除边缘检测带来的杂散响应。

4) 应用双阈值（Double-Threshold）检测来确定真实的和潜在的边缘。

5) 通过抑制孤立的弱边缘最终完成边缘检测。

**（1）图像平滑、去燥**

原理可以参看： [https://mp.csdn.net/postedit/103102498][https_mp.csdn.net_postedit_103102498]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 25][]

**（2）梯度**

对图像平滑后的图像使用 Sobel 算子计算图像梯度和方向

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 26][]

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![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 29][]

**（3）非极大抑制**

![20191120001612674.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 30][]

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**（4）双阈值检测**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3MyOTQ4NzgzMDQ_size_16_color_FFFFFF_t_70 32][]

## 2、代码实例 ##

cv2.Canny(image,            # 输入原图（必须为单通道图）
              threshold1, 
              threshold2,       # 较大的阈值2用于检测图像中明显的边缘
              [, edges[, 
              apertureSize[,    # apertureSize：Sobel算子的大小
              L2gradient ]]])   # 参数(布尔值)：
                                  true： 使用更精确的L2范数进行计算（即两个方向的倒数的平方和再开放），
                                  false：使用L1范数（直接将两个方向导数的绝对值相加）。

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[20191119233911266.png]: https://img-blog.csdnimg.cn/20191119233911266.png
[20191119234009424.png]: https://img-blog.csdnimg.cn/20191119234009424.png
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[Canny]: https://www.cnblogs.com/techyan1990/p/7291771.html
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[https_mp.csdn.net_postedit_103102498]: https://mp.csdn.net/postedit/103102498
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[20191120001612674.png]: https://img-blog.csdnimg.cn/20191120001612674.png
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